Path Following of an Underactuated Autonomous Underwater Vehicle Using Backstepping and Disturbance Observer-Based Sliding Mode Control

Document Type : Research Article

Authors

1 Department of Electrical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran

2 Department of Control Engineering, Malek Ashtar University of Technology, Tehran, Iran.

3 Department of Control Engineering, Malek Ashtar University of Technology, Tehran, Iran

Abstract

In this paper, a new hierarchical robust nonlinear control scheme is designed for the horizontal plane path following control problem of an underactuated autonomous underwater vehicle in the presence of the model uncertainties and fast-time-varying external disturbances. First, the path following error model is established based on the virtual guidance method. Afterwards, the controller design starts at a kinematic level and evolves to a dynamic setting, building on the kinematic controller derived, using backstepping technique and a disturbance observer-based sliding mode control, respectively. A Lyapunov-based stability analysis proves that all the signals are ultimately bounded, and path following errors converge to an arbitrarily small neighborhood of the origin. Following achievements are highlighted in this paper: (I) in order to simplify the control design, the derivative of the virtual control is estimated by the disturbance observer which avoids explosion of complexity without common filtering techniques; (II) the proposed controller can be easily implemented with no information of the bounds on the parameter uncertainties and external disturbances in a continuously changing environment. Furthermore, computer simulations have shown that the overall closed-loop system achieves a good path following performance, which proves the feasibility and good robustness of the proposed control law.  

Keywords

Main Subjects


[1] Z. Peng, J. Wang, J. Wang, Constrained control of autonomous underwater vehicles based on command optimization and disturbance estimation, IEEE Transactions on Industrial Electronics, 66(5) (2019) 3627-3635.
[2] H. Khalil, Nonlinear systems, third ed. New Jersey: Prentice Hall, 2002.
[3] L. Lapierre, D. Soetanto, Nonlinear path-following control of an AUV, Ocean Engineering, 34(11-12) (2007) 1734-1744.
[4] X. Liang, X. Qu, Y. Hou, J. Zhang, Three-dimensional path following control of underactuated autonomous underwater vehicle based on damping backstepping, International Journal of Advanced Robotic Systems, 14(4) (2017) 1-9.
[5] J. Wang, C. Wang, Y. Wei, C. Zhang, Three-Dimensional Path Following of an Underactuated AUV Based on Neuro-Adaptive Command Filtered Backstepping Control, IEEE Access, 6 (2018) 74355-74365.
[6] Z. Zheng, Y. Huang, L. Xie, B. Zhu, Adaptive Trajectory Tracking Control of a Fully Actuated Surface Vessel With Asymmetrically Constrained Input and Output, IEEE Transactions on Control Systems Technology, 26(5) (2018) 1851-1859.
[7] S. Liu, Y. Liu, N. Wang, Nonlinear disturbance observer-based backstepping finite-time sliding mode tracking control of underwater vehicles with system uncertainties and external disturbances, Nonlinear Dynamics, 88 (2017) 465–476.
[8] J. Miao, S. Wang, Z. Zhao, Y. Li, M. Tomovic, Spatial curvilinear path following control of underactuated AUV with multiple uncertainties, ISA Transactions, 67 (2017) 107-130.
[9] Z. Yan, Y. Liu, J. Zhou, D. Wu, Path Following Control of an AUV under the Current Using the SVR-ADRC, Journal of Applied Mathematics, 2014 (2014) 1-12.
[10] Y. Zhang, X. Wang, S. Wang, J. Miao, DO-LPV-based robust 3D path following control of underactuated autonomous underwater vehicle with multiple uncertainties, ISA Transactions, 101 (2020) 189-203.
[11] R. Cui, L. Chen, C. Yang, M. Chen, Extended State Observer-Based Integral Sliding Mode Control for an Underwater Robot With Unknown Disturbances and Uncertain Nonlinearities, IEEE Transactions on Industrial Electronics, 64(8) (2017) 6785-6795.
[12] J. Guerrero, J. Torres, V. Creuze, A. Chemori, Adaptive disturbance observer for trajectory tracking control of underwater vehicles, Ocean Engineering, 200 (2020).
[13] B. Subudhi, K. Mukherjee, S. Ghosh, A static output feedback control design for path following of autonomous underwater vehicle in vertical plane, Ocean Engineering, 63 (2013) 72–76.
[14] J. Refsnes, A. Sorensen, K. Pettersen, Model-based output feedback control of slender-body underactuated AUVs: theory and experiments, IEEE Transactions on Control Systems Technology, 16(5) (2008) 930-946.
[15] L. Zhang, X. Qi, Y. Pang, Adaptive output feedback control based on DRFNN for AUV, Ocean Engineering, 36(9-10) (2009).
[16] N. Kumar, M. Rani, An efficient hybrid approach for trajectory tracking control of autonomous underwater vehicles, Applied Ocean Research, 95 (2020) 102053.
[17] K. Do, J. Pan, Z. Jiang, Robust and adaptive path following for underactuated autonomous underwater vehicles, Ocean Engineering, 31(16) (2004) 1967-1997.
[18] J. Xu, M. Wang, L. Qiao, Dynamical sliding mode control for the trajectory tracking of underactuated unmanned underwater vehicles, Ocean Engineering, 105 (2015) 54–63.
[19] X. Liang, X. Qu, L. Wan, Q. Ma, Three-Dimensional Path Following of an Underactuated AUV Based on Fuzzy Backstepping Sliding Mode Control, International Journal of Fuzzy Systems, 20 (2018) 640-649.
[20] T. Elmokadem, M. Zribi, K. Youcef-Toumi, Trajectory tracking sliding mode control of underactuated AUVs, Nonlinear Dynamics, 84 (2015) 1079–1091.
[21] H. Joe, M. Kim, S. Yu, Second-order sliding-mode controller for autonomous underwater vehicle in the presence of unknown disturbances, Nonlinear Dynamics, 78 (2014) 183–196.
[22] G. Zhang, H. Huang, H. Qin, L. Wan, Y. Li, J. Cao, Y. Su, A novel adaptive second order sliding mode path following control for a portable AUV, Ocean Engineering, 151 (2018) 82–92.
[23] J. Zhou, X. Zhao, T. Chen, Z. Yan, Z. Yang, Trajectory Tracking Control of an Underactuated AUV Based on Backstepping Sliding Mode With State Prediction, IEEE Access, 7 (2019) 181983-181993.
[24] B. Patre, P. Londhe, R. Nagarale, Fuzzy Sliding Mode Control for Spatial Control of Large Nuclear Reactor, IEEE Transactions on Nuclear Science, 62(5) (2015) 2255-2265.
[25] Z. Yan, M. Wang, J. XU, Robust adaptive sliding mode control of underactuated autonomous underwater vehicles with uncertain dynamics, Ocean Engineering, 173 (2019) 802-809.
[26] K. Pettersen, O. Egeland, Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle, IEEE Transactions on Automatic Control, 44(1) (1999) 112-115.
[27] W. Chen, Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles, Journal of Guidance, Control and Dynamics, 26(1) (2003) 161-166.
[28] M. Corless, G. Leitman, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Transactions on Automatic Control, 26(5) (1981) 1139-1144.
[29] C. Yu, X. Xiang, L. Lapierre, Q. Zhang, Robust Magnetic Tracking of Subsea Cable by AUV in the Presence of Sensor Noise and Ocean Currents, IEEE Journal of Oceanic Engineering, 43(2) (2018) 311-322.